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Diffstat (limited to 'sysdeps/ia64/fpu/e_exp2.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_exp2.S | 564 |
1 files changed, 0 insertions, 564 deletions
diff --git a/sysdeps/ia64/fpu/e_exp2.S b/sysdeps/ia64/fpu/e_exp2.S deleted file mode 100644 index 54f652e384..0000000000 --- a/sysdeps/ia64/fpu/e_exp2.S +++ /dev/null @@ -1,564 +0,0 @@ -.file "exp2.s" - - -// Copyright (c) 2000 - 2005, Intel Corporation -// All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation -// -// Redistribution and use in source and binary forms, with or without -// modification, are permitted provided that the following conditions are -// met: -// -// * Redistributions of source code must retain the above copyright -// notice, this list of conditions and the following disclaimer. -// -// * Redistributions in binary form must reproduce the above copyright -// notice, this list of conditions and the following disclaimer in the -// documentation and/or other materials provided with the distribution. -// -// * The name of Intel Corporation may not be used to endorse or promote -// products derived from this software without specific prior written -// permission. - -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS -// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY -// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// -// Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://www.intel.com/software/products/opensource/libraries/num.htm. -// -// History -//============================================================== -// 08/25/00 Initial version -// 05/20/02 Cleaned up namespace and sf0 syntax -// 09/05/02 Improved performance -// 01/17/03 Fixed to call error support when x=1024.0 -// 03/31/05 Reformatted delimiters between data tables -// -// API -//============================================================== -// double exp2(double) -// -// Overview of operation -//============================================================== -// Background -// -// Implementation -// -// Let x= (K + fh + fl + r), where -// K is an integer, fh= 0.b1 b2 b3 b4 b5, -// fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0), -// and |r|<2^{-11} -// Th is a table that stores 2^fh (32 entries) rounded to -// double extended precision (only mantissa is stored) -// Tl is a table that stores 2^fl (32 entries) rounded to -// double extended precision (only mantissa is stored) -// -// 2^x is approximated as -// 2^K * Th [ f ] * Tl [ f ] * (1+c1*r+c2*r^2+c3*r^3+c4*r^4) - -// Note: We use the following trick to speed up conversion from FP to integer: -// -// Let x = K + r, where K is an integer, and |r| <= 0.5 -// Let N be the number of significand bits for the FP format used -// ( N=64 for double-extended, N=53 for double) -// -// Then let y = 1.5 * 2^(N-1) + x for RN mode -// K = y - 1.5 * 2^(N-1) -// r = x - K -// -// If we want to obtain the integer part and the first m fractional bits of x, -// we can use the same trick, but with a constant of 1.5 * 2^(N-1-m): -// -// Let x = K + f + r -// f = 0.b_1 b_2 ... b_m -// |r| <= 2^(-m-1) -// -// Then let y = 1.5 * 2^(N-1-m) + x for RN mode -// (K+f) = y - 1.5 * 2^(N-1-m) -// r = x - K - - -// Special values -//============================================================== -// exp2(0)= 1 -// exp2(+inf)= inf -// exp2(-inf)= 0 -// - -// Registers used -//============================================================== -// r2-r3, r14-r40 -// f6-f15, f32-f45 -// p6-p8, p12 -// - - -GR_TBL_START = r2 -GR_LOG_TBL = r3 - -GR_OF_LIMIT = r14 -GR_UF_LIMIT = r15 -GR_EXP_CORR = r16 -GR_F_low = r17 -GR_F_high = r18 -GR_K = r19 -GR_Flow_ADDR = r20 - -GR_BIAS = r21 -GR_Fh = r22 -GR_Fh_ADDR = r23 -GR_EXPMAX = r24 -GR_EMIN = r25 - -GR_ROUNDVAL = r26 -GR_MASK = r27 -GR_KF0 = r28 -GR_MASK_low = r29 -GR_COEFF_START = r30 - -GR_SAVE_B0 = r33 -GR_SAVE_PFS = r34 -GR_SAVE_GP = r35 -GR_SAVE_SP = r36 - -GR_Parameter_X = r37 -GR_Parameter_Y = r38 -GR_Parameter_RESULT = r39 -GR_Parameter_TAG = r40 - - -FR_X = f10 -FR_Y = f1 -FR_RESULT = f8 - - -FR_COEFF1 = f6 -FR_COEFF2 = f7 -FR_R = f9 - -FR_KF0 = f12 -FR_COEFF3 = f13 -FR_COEFF4 = f14 -FR_UF_LIMIT = f15 - -FR_OF_LIMIT = f32 -FR_EXPMIN = f33 -FR_ROUNDVAL = f34 -FR_KF = f35 - -FR_2_TO_K = f36 -FR_T_low = f37 -FR_T_high = f38 -FR_P34 = f39 -FR_R2 = f40 - -FR_P12 = f41 -FR_T_low_K = f42 -FR_P14 = f43 -FR_T = f44 -FR_P = f45 - - -// Data tables -//============================================================== - -RODATA - -.align 16 - -LOCAL_OBJECT_START(poly_coeffs) - -data8 0x3fac6b08d704a0c0, 0x3f83b2ab6fba4e77 // C_3 and C_4 -data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1 -data8 0xf5fdeffc162c7541, 0x00003ffc // C_2 -LOCAL_OBJECT_END(poly_coeffs) - - -LOCAL_OBJECT_START(T_table) - -// 2^{0.00000 b6 b7 b8 b9 b10} -data8 0x8000000000000000, 0x8016302f17467628 -data8 0x802c6436d0e04f50, 0x80429c17d77c18ed -data8 0x8058d7d2d5e5f6b0, 0x806f17687707a7af -data8 0x80855ad965e88b83, 0x809ba2264dada76a -data8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77f -data8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763e -data8 0x810b40a1d81406d4, 0x81219f24a5baa59d -data8 0x813801881d886f7b, 0x814e67cceb90502c -data8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47 -data8 0x8191b1ea15813bfd, 0x81a827baf7838b78 -data8 0x81bea1708dde6055, 0x81d51f0b8557ec1c -data8 0x81eba08c8ad4536f, 0x820225f44b55b33b -data8 0x8218af4373fc25eb, 0x822f3c7ab205c89a -data8 0x8245cd9ab2cec048, 0x825c62a423d13f0c -data8 0x8272fb97b2a5894c, 0x828998760d01faf3 -data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906 -// -// 2^{0.b1 b2 b3 b4 b5} -data8 0x8000000000000000, 0x82cd8698ac2ba1d7 -data8 0x85aac367cc487b14, 0x88980e8092da8527 -data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0 -data8 0x91c3d373ab11c336, 0x94f4efa8fef70961 -data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538 -data8 0x9ef5326091a111ad, 0xa27043030c496818 -data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8 -data8 0xad583eea42a14ac6, 0xb123f581d2ac258f -data8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9 -data8 0xbd08a39f580c36be, 0xc12c4cca66709456 -data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2 -data8 0xce248c151f8480e3, 0xd2a81d91f12ae45a -data8 0xd744fccad69d6af4, 0xdbfbb797daf23755 -data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8 -data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cb -data8 0xf5257d152486cc2c, 0xfa83b2db722a033a -LOCAL_OBJECT_END(T_table) - - - -.section .text -GLOBAL_LIBM_ENTRY(exp2) - - -{.mfi - alloc r32= ar.pfs, 1, 4, 4, 0 - // will continue only for non-zero normal/denormal numbers - fclass.nm p12, p0= f8, 0x1b - // GR_TBL_START= pointer to C_1...C_4 followed by T_table - addl GR_TBL_START= @ltoff(poly_coeffs), gp -} -{.mlx - mov GR_OF_LIMIT= 0xffff + 10 // Exponent of overflow limit - movl GR_ROUNDVAL= 0x5a400000 // 1.5*2^(63-10) (SP) -} -;; - -// Form special constant 1.5*2^(63-10) to give integer part and first 10 -// fractional bits of x -{.mfi - setf.s FR_ROUNDVAL= GR_ROUNDVAL // Form special constant - fcmp.lt.s1 p6, p8= f8, f0 // X<0 ? - nop.i 0 -} -{.mfb - ld8 GR_COEFF_START= [ GR_TBL_START ] // Load pointer to coeff table - nop.f 0 - (p12) br.cond.spnt SPECIAL_exp2 // Branch if nan, inf, zero -} -;; - -{.mlx - setf.exp FR_OF_LIMIT= GR_OF_LIMIT // Set overflow limit - movl GR_UF_LIMIT= 0xc4866000 // (-2^10-51) = -1075 -} -;; - -{.mfi - ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4 - fma.s0 f8= f8, f1, f0 // normalize x - nop.i 0 -} -;; - -{.mmi - setf.s FR_UF_LIMIT= GR_UF_LIMIT // Set underflow limit - ldfe FR_COEFF1= [ GR_COEFF_START ], 16 // load C_1 - mov GR_EXP_CORR= 0xffff-126 -} -;; - -{.mfi - ldfe FR_COEFF2= [ GR_COEFF_START ], 16 // load C_2 - fma.s1 FR_KF0= f8, f1, FR_ROUNDVAL // y= x + 1.5*2^(63-10) - nop.i 0 -} -;; - -{.mfi - mov GR_MASK= 1023 - fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL // (K+f) - mov GR_MASK_low= 31 -} -;; - -{.mfi - getf.sig GR_KF0= FR_KF0 // (K+f)*2^10= round_to_int(y) - fcmp.ge.s1 p12, p7= f8, FR_OF_LIMIT // x >= overflow threshold ? - add GR_LOG_TBL= 256, GR_COEFF_START // Pointer to high T_table -} -;; - -{.mmi - and GR_F_low= GR_KF0, GR_MASK_low // f_low - and GR_F_high= GR_MASK, GR_KF0 // f_high*32 - shr GR_K= GR_KF0, 10 // K -} -;; - -{.mmi - shladd GR_Flow_ADDR= GR_F_low, 3, GR_COEFF_START // address of 2^{f_low} - add GR_BIAS= GR_K, GR_EXP_CORR // K= bias-2*63 - shr GR_Fh= GR_F_high, 5 // f_high -} -;; - -{.mfi - setf.exp FR_2_TO_K= GR_BIAS // 2^{K-126} - fnma.s1 FR_R= FR_KF, f1, f8 // r= x - (K+f) - shladd GR_Fh_ADDR= GR_Fh, 3, GR_LOG_TBL // address of 2^{f_high} -} -{.mlx - ldf8 FR_T_low= [ GR_Flow_ADDR ] // load T_low= 2^{f_low} - movl GR_EMIN= 0xc47f8000 // EMIN= -1022 -} -;; - -{.mfi - ldf8 FR_T_high= [ GR_Fh_ADDR ] // load T_high= 2^{f_high} - (p7) fcmp.lt.s1 p12, p7= f8, FR_UF_LIMIT // x<underflow threshold ? - nop.i 0 -} -;; - -{.mfi - setf.s FR_EXPMIN= GR_EMIN // FR_EXPMIN= EMIN - fma.s1 FR_P34= FR_COEFF4, FR_R, FR_COEFF3 // P34= C_3+C_4*r - nop.i 0 -} -{.mfb - nop.m 0 - fma.s1 FR_R2= FR_R, FR_R, f0 // r*r - (p12) br.cond.spnt OUT_RANGE_exp2 -} -;; - -{.mfi - nop.m 0 - fma.s1 FR_P12= FR_COEFF2, FR_R, FR_COEFF1 // P12= C_1+C_2*r - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fma.s1 FR_T_low_K= FR_T_low, FR_2_TO_K, f0 // T= 2^{K-126}*T_low - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fma.s1 FR_P14= FR_R2, FR_P34, FR_P12 // P14= P12+r2*P34 - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fma.s1 FR_T= FR_T_low_K, FR_T_high, f0 // T= T*T_high - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fcmp.lt.s0 p6, p8= f8, FR_EXPMIN // underflow (x<EMIN) ? - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fma.s1 FR_P= FR_P14, FR_R, f0 // P= P14*r - nop.i 0 -} -;; - -{.mfb - nop.m 0 - fma.d.s0 f8= FR_P, FR_T, FR_T // result= T+T*P - (p8) br.ret.sptk b0 // return -} -;; - -{.mfb - (p6) mov GR_Parameter_TAG= 162 - nop.f 0 - (p6) br.cond.sptk __libm_error_region -} -;; - - -SPECIAL_exp2: -{.mfi - nop.m 0 - fclass.m p6, p0= f8, 0x22 // x= -Infinity ? - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fclass.m p7, p0= f8, 0x21 // x= +Infinity ? - nop.i 0 -} -;; - -{.mfi - nop.m 0 - fclass.m p8, p0= f8, 0x7 // x= +/-Zero ? - nop.i 0 -} -{.mfb - nop.m 0 - (p6) mov f8= f0 // exp2(-Infinity)= 0 - (p6) br.ret.spnt b0 -} -;; - -{.mfb - nop.m 0 - nop.f 0 - (p7) br.ret.spnt b0 // exp2(+Infinity)= +Infinity -} -;; - -{.mfb - nop.m 0 - (p8) mov f8= f1 // exp2(+/-0)= 1 - (p8) br.ret.spnt b0 -} -;; - -{.mfb - nop.m 0 - fma.d.s0 f8= f8, f1, f0 // Remaining cases: NaNs - br.ret.sptk b0 -} -;; - - -OUT_RANGE_exp2: - -// overflow: p8= 1 - -{.mii - (p8) mov GR_EXPMAX= 0x1fffe - nop.i 0 - nop.i 0 -} -;; - -{.mmb - (p8) mov GR_Parameter_TAG= 161 - (p8) setf.exp FR_R= GR_EXPMAX - nop.b 999 -} -;; - -{.mfi - nop.m 999 - (p8) fma.d.s0 f8= FR_R, FR_R, f0 // Create overflow - nop.i 999 -} -// underflow: p6= 1 -{.mii - (p6) mov GR_Parameter_TAG= 162 - (p6) mov GR_EXPMAX= 1 - nop.i 0 -} -;; - -{.mmb - nop.m 0 - (p6) setf.exp FR_R= GR_EXPMAX - nop.b 999 -} -;; - -{.mfb - nop.m 999 - (p6) fma.d.s0 f8= FR_R, FR_R, f0 // Create underflow - nop.b 0 -} -;; - -GLOBAL_LIBM_END(exp2) - - -LOCAL_LIBM_ENTRY(__libm_error_region) - -.prologue -{.mfi - add GR_Parameter_Y= -32, sp // Parameter 2 value - nop.f 0 -.save ar.pfs, GR_SAVE_PFS - mov GR_SAVE_PFS= ar.pfs // Save ar.pfs -} - -{.mfi -.fframe 64 - add sp= -64, sp // Create new stack - nop.f 0 - mov GR_SAVE_GP= gp // Save gp -} -;; - -{.mmi - stfd [ GR_Parameter_Y ]= FR_Y, 16 // STORE Parameter 2 on stack - add GR_Parameter_X= 16, sp // Parameter 1 address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0= b0 // Save b0 -} -;; - -.body -{.mib - stfd [ GR_Parameter_X ]= FR_X // STORE Parameter 1 on stack - add GR_Parameter_RESULT= 0, GR_Parameter_Y // Parameter 3 address - nop.b 0 -} -{.mib - stfd [ GR_Parameter_Y ]= FR_RESULT // STORE Parameter 3 on stack - add GR_Parameter_Y= -16, GR_Parameter_Y - br.call.sptk b0= __libm_error_support# // Call error handling function -} -;; - -{.mmi - add GR_Parameter_RESULT= 48, sp - nop.m 0 - nop.i 0 -} -;; - -{.mmi - ldfd f8= [ GR_Parameter_RESULT ] // Get return result off stack -.restore sp - add sp= 64, sp // Restore stack pointer - mov b0= GR_SAVE_B0 // Restore return address -} -;; - -{.mib - mov gp= GR_SAVE_GP // Restore gp - mov ar.pfs= GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return -} -;; - - -LOCAL_LIBM_END(__libm_error_region) - -.type __libm_error_support#, @function -.global __libm_error_support# |